Atkin-Lehner |
3+ 7- 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
112749d |
Isogeny class |
Conductor |
112749 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
207360 |
Modular degree for the optimal curve |
Δ |
-20175771600621 = -1 · 33 · 78 · 133 · 59 |
Discriminant |
Eigenvalues |
1 3+ 1 7- 1 13+ 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-5317,260422] |
[a1,a2,a3,a4,a6] |
Generators |
[-162:4883:8] |
Generators of the group modulo torsion |
j |
-141339344329/171491229 |
j-invariant |
L |
7.7724136934646 |
L(r)(E,1)/r! |
Ω |
0.61859164475889 |
Real period |
R |
3.1411730816353 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001672 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16107e1 |
Quadratic twists by: -7 |